As noted in the introduction, these 3-point operators (and their shadow conjugates) are already known from the triple-\(K\)  representation of the 3-point function. In [1]}, [2]}, the Bessel shift operators
\(\mathcal {L}_i = -\frac{1}{p_i}\frac{\partial }{\partial p_i}, \qquad \mathcal {R}_i = 2\beta _i - p_i\frac{\partial }{\partial p_i} = p_i^{2\beta _i+2}\,\mathcal {L}_i \,p_i^{-2\beta _i},\qquad \beta _i=\Delta _i-\frac{d}{2}\) 
